Perhaps they are in the habit of searching at the book-in desk, being a restricted area etc? I would have patted him down at point of arrest and I think the officer may have. He refers to the perp having stuff in his pockets so at some stage he must have felt or suspected something. Still, it would have been better to search him while he was handcuffed!
The grab the knife arm method was pretty much all he had as options given the restricted area. I think if MA instructors insist you can;t grab the weapon hand/arm they are limiting themselves to the stand-off/duel scenario as well as believing every attacker will be thinking cool and rational stragey type thoughts like they do every time they run the scenario in their heads.
Note the knife came out at 0:03:12 into the video, the officer had the arm grabbed by 0:03:13 and the subject was disarmed and under control by 0:03:16. (Under control includes the big cop sitting on the perp's head after he we went over the desk to his mates assistance, hehehehehehehe) So less than 4 seconds, not bad. The initial presenting and reacting was a 1 second sequence. Like they say, it all happened so fast!
Cheers, Redcap